Such a transmission is for example necessary, when a transmitter transmits a data packet common for a plurality of receivers. In this case, the list of identifiers of these receivers is generally included in the header of the data packet to be transmitted and this header is then transmitted to the whole of the receivers of the computer network.
Upon receiving this header, each receiver extracts the list of identifiers from it and if its identifier is in the list, this receiver continues to receive the data packet entirely. In the opposite case, the receiver ignores the reception of the packet or transmits it to another receiver without having read it.
In computer networks of large dimensions, the identifier of a receiver is generally represented by a number with a significant length or by a complex combination of numbers and letters or other symbols. The size of the header of a data packet including a list of such identifiers therefore becomes very substantial and sometimes exceeds the size of the remainder of the packet. This notably leads to an overload of the computer network.
Different transmission techniques allowing reduction in the size of such a list of identifiers exist in the state of the art.
Notably, it is common to encode a list of identifiers, all different, belonging to a larger set of known identifiers.
Coding theory shows moreover that the minimum number of bits required for transmitting a list of identifiers belonging to a larger set of identifiers is equal to the following expression:NB=┌log2CNP┐
with
┌.┐ referring to the excess integer portion,
NB referring to the number of bits,
P referring to the number of addressees,
N referring to the total number of receivers, and
CNP referring to the number of sub-sets of cardinal P, in a set with cardinal N.
Optimum encoding is an encoding giving the possibility of obtaining a code length of this size. Optimum encoding therefore gives a minimum theoretical size code for a list of identifiers belonging to a larger set of identifiers. This minimum theoretical size in particular allows efficient transmission of a list of identifiers even in a computer network of a large size.
However, this solution is not completely satisfactory.
Notably, the use of optimum encoding generally requires maintaining in the memory of the transmitter and of each receiver a coding table including all the matches between the codes and the identifiers. The size of this table is very large even for a computer network of a reasonable size.